As for the moment, VOX is designed to start with an internal speaker as default.
It means that you can see all available outputs in the list and choose the one you need at any time, but it should be done manually or by choosing "Same as System" option.
If you have plenty of outputs connected, how would VOX know what is the preferable one to choose automatically?
Still, we are having this feature you are talking about on our roadmap, to make VOX remember chosen output and start with it.
If you have something else to assist with, please contact our tech. support in direct: https://vox.rocks/support
Sure it will help to figure it out.